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August, 2005
An Options-Based Approach to Evaluating the Risk of Fannie Mae and Freddie Mac
Deborah Lucas* Robert McDonald**
Abstract Fannie Mae and Freddie Mac assume a significant amount of interest and prepayment risk and all of the credit risk for about half of the $8 trillion U.S. residential mortgage market. Their hybrid government-private status, and the perception that they are too big to fail, make them a potentially large, but largely unaccounted for, risk to the federal government. Measuring the size and risk of this liability is technically difficult, but important for the debate over the appropriate regulation of these institutions. Here we take an options pricing approach to evaluating these costs and risks. Under the base case assumptions, the estimated value of the guarantees is $7.9 billion over 10 years, with a combined .5 percent value at risk of $122 billion. We evaluate the sensitivity of these estimates to various modeling assumptions, and also to the regulatory regime, including forbearance policies and capital requirements. The analysis highlights the benefits, but also the challenges, of taking on options-based approach to evaluating the value of federal credit guarantees. *Northwestern University and the NBER. *Northwestern University This paper was prepared for the 2005 Carnegie Rochester Public Policy Conference. We thank Wendy Kiska, Marvin Phaup and David Torregrosa for their generous help and suggestions on this project, and Robin Seiler for useful conversations. We also thank conference participants, and especially Marvin Goodfriend, Andreas Lehnart, Wayne Passmore and George Pennachi for their detailed comments.
2
1. Introduction
Fannie Mae and Freddie Mac (F&F) assume a significant amount of interest and prepayment risk,
and all of the credit risk, for about half of the roughly $8 trillion U.S. residential mortgage
market. Their hybrid government-private status, and the likelihood that they would not be
allowed to fail because of the disruption it would cause to housing and financial markets, make
them a potentially costly risk to the federal government, and ultimately to taxpayers.
How large is this risk? The answer, although much debated in the literature (e.g., CBO (2001),
Jaffee (2003), Naranjo and Toevs (2002), Hubbard(2004), Passmore (2005), Stiglitz et. al.
(2002))1, remains poorly understood for a variety of reasons including limited regulatory
oversight and financial disclosure; and the inherent difficulties in modeling F&F’s risk exposure.
Compared to commercial banks and thrifts, F&F are lightly regulated. Their regulator, the Office
of Federal Housing Enterprise Oversight (OFHEO)2, cannot force prompt closure, has limited
modeling capabilities, and has very little latitude in adjusting capital requirements (Falcon
(2004)). The absence of an explicit federal guarantee means that no cost for F&F is recorded in
the federal budget, diluting the incentive for lawmakers to strengthen regulatory oversight or
increase legislative restrictions on risk-taking. F&F’s charter act exempts them from SEC
disclosure requirements, although they voluntarily comply with a number of its provisions for
equity. Modeling F&F’s risk exposure is complicated by its sensitivity to the poorly measured
tails of the distributions of interest rates and housing prices. Even if those risks could be
accurately assessed, F&F’s extensive and non-transparent use of derivatives and their
complicated liability structures make it impractical to model their risk exposure using reported
on- and off-balance-sheet quantities.
This paper takes an options-based approach to evaluating two related questions: what is the
insurance value of the implicit government guarantee to Fannie Mae and Freddie Mac, and how
does the distribution of possible losses change under alternative policy regimes? An advantage of
1 Few disinterested parties participate in this debate. Many of the studies that found costs to be low were commissioned by the GSEs (e.g., Hubbard (2004), Naranjo and Toevs (2002), and Stiglitz et. al. (2002)) whereas the studies that provided evidence for higher costs were under the auspices of federal government entities (e.g., CBO (2001) and Passmore (2003) is at the Federal Reserve Board of Governors.) Feldman (1999) surveys the results of older studies. 2 OFHEO is part of the Department of Housing and Urban Development (HUD), and agency whose primary mission is to promote affordable housing, not financial market stability.
3
this approach is that it requires making assumptions about a relatively limited set of variables –
firm asset variability, debt policy, and the trigger point for bankruptcy. It avoids having to
explicitly model F&F’s use of derivatives or the many sources of risk affecting their solvency,
since these factors are implicitly reflected in the distribution of firm asset and liability values.
Further, the option approach properly incorporates the price of market risk into the estimate of the
guarantee value. This is important because credit guarantees are equivalent to highly levered
positions in the assets of the guaranteed firms, and hence their value reflects their considerable
market risk (CBO (2004b)).
Despite the relative simplicity of an options-based approach, serious difficulties remain. These
include: whether the relatively short historical time series observed provides information about
the tails of the relevant statistical distributions; the extent to which F&F could and would adjust
their investment policy and debt in response to a rapid change in circumstances; and how quickly
F&F would be forced to cease operating in the event of serious financial distress. Because of
these uncertainties, rather than emphasizing a set of fixed assumptions, we focus on the
sensitivity of cost estimates and value at risk (VaR) to a variety of assumptions. The options-
based estimates also are compared to earlier estimates of guarantee value based on credit spreads
(Passmore (2005), and CBO (2001)), and also other volatility-based approaches (Stiglitz et. al.
(2002), Hubbard (2004)).
To briefly summarize the main findings, under the base case assumptions the combined value of
the implicit guarantee to F&F over a 10-year horizon is $7.9 billion. The value at risk at the .5
percent level is $74 billion for Fannie and $48 for Freddie. Extending the horizon to 25 years
increases the estimated guarantee value to $28 billion, and increases the value at risk to $89
billion and $60 billion respectively. A novel feature of the analysis is to increase the conditional
volatility of assets in periods of distress. We show that this significantly increases guarantee
value and value at risk, although it generates an undetectable increase in measured asset volatility
in time series data. Different policy options for limiting risk have very different effects.
Increasing capital requirements significantly lowers guarantee value, but has a relatively small
effect on catastrophic outcomes, as measured by the value at risk. Conversely, a reduction in
regulatory forbearance -- either in the form of more frequent monitoring or a more stringent
bankruptcy trigger -- has a minimal effect on guarantee value, but significantly reduces the
probability of a catastrophic outcome.
Deleted: 1
4
The remainder of the paper is organized as follows: In Section 2 we provide some background on
Fannie and Freddie. In Section 3 we introduce the basic model, discuss some of the critical
sensitivities, and lay out the alternative assumptions that are considered. Quantitative results are
presented in Section 4. Section 5 concludes with a discussion of policy options to reduce the risk
exposure from these entities.
2. Background
Fannie Mae and Freddie Mac were created by acts of Congress to provide liquidity and stability
in the home mortgage market. Fannie Mae was originally created as a wholly owned government
corporation in 1938, for the purpose of buying mortgages from originators and holding them in its
portfolio. It was converted into a GSE (Government Sponsored Enterprise) in 1968. Freddie Mac
was created in 1970 as part of the Federal Home Loan Bank System to purchase mortgages from
thrifts. Rather than holding mortgages in its portfolio, Freddie Mac pooled the mortgages and
attached a guarantee for credit risk. Claims to the cash flows from the insured mortgage pools
were sold to investors, creating mortgage-backed securities (MBS).
GSEs are hybrids of private corporations and federal entities. Although they are required to issue
their debt securities with the explicit statement that they do not bear a government guarantee,
their many federal ties convince investors otherwise, as evidenced by the relatively narrow spread
between GSE and Treasury debt issues compared to other financial institutions. According to the
Congressional Budget Office (2001), these federal connections include that they are chartered by
federal statute, exempt from state and local income taxes, exempt from the Securities and
Exchange Commission's (SEC's) registration requirements and fees, and may use the Federal
Reserve as their fiscal agent. The U.S. Treasury is authorized to lend $2.25 billion to each of
them. GSE debt is eligible for use as collateral for public deposits, for unlimited investment by
federally chartered banks and thrifts, and for purchase by the Federal Reserve in open-market
operations. GSE securities are explicitly government securities under the Securities Exchange Act
of 1934 and are exempt from the provisions of many state investor protection laws.
Concern about systemic risk has escalated along with the rapid growth of these enterprises (see
Frame and White (2005) for a recent survey). Their assets on-balance sheet grew rapidly through
2003, but fell slightly in 2004 to combined liabilities of $1.677 trillion (Table 1). The risk
represented by on-balance sheet holdings is considerably greater than for the MBS they
5
guarantee. Their mortgage holdings are financed largely with fixed rate debt of various
maturities, creating exposure to interest rate and prepayment risk that is partially hedged with
derivatives. The exposure on MBS is limited to credit risk, which causes little concern because of
the collateral value of houses and historically low credit losses. Nevertheless, a large negative
shock to house prices could lead to significant losses on the $2.255 trillion of MBSs guaranteed
by the two firms, as well as on their balance sheet holdings. A further concern is that the implicit
government subsidy accrues to F&F’s shareholders rather than to the housing market.
Historically these firms have been extremely profitable for their investors (see Figure 1). The
returns on the two firms are highly correlated, confirming that they are affected by common risk
factors. The correlation in monthly data from October 1989 to December 2004 is 79.5 percent.
2.1 Risk Experience and Disclosure
The potential susceptibility of the GSEs to economic shocks, particularly when mortgages are
held on-balance-sheet rather than securitized, was demonstrated during the late 1970s and early
1980s. As for the savings and loan industry, high and volatile interest rates weakened Fannie Mae
as the value of 30-year mortgages fell and the cost of financing increased. Because interest rate
and prepayment risk are transferred to the buyers of MBS, Freddie Mac was much less exposed to
interest rate risk during this earlier time period, and hence was less adversely affected than was
Fannie Mae.
This experience caused Fannie Mae to take measures to reduce balance sheet risk exposure, and
beginning in the early 1980s, it rapidly increased its reliance on MBS. For both companies,
however, the ratio of mortgages held in portfolio to MBSs guaranteed only against credit losses
grew rapidly in the 1990s, and has flattened out since 2000 (see Figure 2, which is based on Table
1).
6
TABLE 1. OUTSTANDING MBS AND DEBT, YEAR-END 1985-2004 (In billions of dollars)
Fannie Mae Freddie Mac MBSa Debtb MBSa Debtb
1985 55 94 100 13 1986 96 94 169 15 1987 136 97 213 20 1988 170 105 226 27 1989 217 116 273 26 1990 288 123 316 31 1991 355 134 359 30 1992 424 166 408 30 1993 471 201 439 50 1994 486 257 461 93 1995 513 299 459 120 1996 548 331 473 157 1997 579 370 476 173 1998 637 460 478 287 1999 679 548 538 361 2000 707 643 576 427 2001 859 763 653 578 2002 1,029 851 749 666 2003 1,300 962 773 740 2004 1,403
945
852
732
SOURCE: Congressional Budget Office based on data from the Department of Housing and Urban Development’s Office of Federal Housing Enterprise Oversight, and the Federal Housing Finance Board. The 2004 numbers are based on data from Fannie Mae and Freddie Mac. a. MBSs = mortgage-backed securities issued by the enterprise; excludes holdings of the enterprise’s own MBSs held in its portfolio. These are off-balance sheet, with exposure only to credit risk. b.On-balance sheet debt, financing primarily mortgages with exposure to interest rate, pre-payment, and credit risk. * As of June 30, 2004, data from FHLB Office of Finance.
7
Figure 1: Cumulative Monthly ReturnsSept. 1989 - Dec. 2004
02468
10121416
Aug-89
Aug-90
Aug-91
Aug-92
Aug-93
Aug-94
Aug-95
Aug-96
Aug-97
Aug-98
Aug-99
Aug-00
Aug-01
Aug-02
Aug-03
Aug-04
Date
Ret
urns Fannie
FreddieS&P
Figure 2: Ratio of Outstanding Debt to MBS
0.0020.0040.0060.0080.00
100.00120.00140.00160.00180.00
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
Year
Per
cent FNM ratio
FRE ratio
Although the growth in portfolio holdings appears to represent a considerable increase in risk
taking over the last decade, Fannie Mae and Freddie Mac take measures to hedge their exposure
using derivatives such as swaps, swaptions, and callable debt, as well as dynamic hedging
strategies (see Jaffee (2003) for a more detailed discussion). The effectiveness of these hedges is
difficult to evaluate because of the very limited risk disclosure by both firms, and because there
8
has not been a shock large enough to test the functioning of the derivatives markets upon which
the hedges rely.
One measure of risk exposure that both firms report is their duration gap, which measures the
difference in the sensitivity of portfolio assets and liabilities to changes in interest rates. For
instance, a 6 month duration gap means that a 1 percent increase in interest rates will cause the
value of assets to fall by about ½ percent more than the value of liabilities, thereby eroding
capital by an amount equal to ½ percent of assets. The measure proved informative in September
of 2002, when Fannie reported that its duration gap had ballooned to 14 months, well outside its
target range of less than 6 months. Capital markets responded to this information, as reflected in
the increase in the implied volatility of Fannie’s equity value at that time (see Figure 3). Implied
volatilities are derived from options price data using an options pricing model. The return of
implied volatilities to normal levels suggests that the concerns raised by the event were short-
lived.
F&F also present a “fair value balance sheet” designed to give a more accurate picture of their
economic situation than their official balance sheet that reflects accounting conventions (such as
mixing market and book values) that can be misleading. While Freddie reports its fair value
quarterly, Fannie reports it only annually.
9
Although F&F are exempt from SEC registration requirements and fees, recently Fannie opted to
register their common stock with the SEC, and Freddie has expressed the intention to follow. In
doing so, information from Form 10k and other mandatory disclosures for publicly traded firms
will become available, but these reports have only limited quantitative information on derivatives,
and will add little to disclosures already made by the enterprises. Neither registers their debt or
MBS securities with the SEC.
Credit ratings provide an additional external evaluation of default risk, and have been used in
some past studies as the basis for estimating the government subsidy (CBO (2001), Passmore
(2005)). The ratings agencies have refined their analysis in recent years, and now make a clear
distinction between a rating that reflects the risk to investors in agency debt securities and the
companies’ stand-alone risk. Moody’s rating, taking into account the regulatory regime and
implicit guarantee, is AAA for the unsecured debt of both firms, and P-1 for short-term issues.
However the “bank financial strength rating,” which corresponds more closely to a measure of
the risk to the government, was recently lowered to B+ from and A- for Fannie. For Freddie the
bank financial strength rating is A-. The credit default swap market offers another piece of data
on how the risk of F&F compare to other financial institutions. Credit default swaps (CDS) are
Figure 3: The Effect of the 9/02 Spike in Fannie's Duration Gap on Implied Volatility Differentials
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
7/1/2002 8/1/2002 9/1/2002 10/1/2002 11/1/2002 12/1/2002
Date
Implied volatility
Fre 30-day implied vol FNMA 30-day implied vol
10
derivatives that make a payment to the protection buyer if there is a default event on an
underlying security, in exchange for a fixed premium payment to the protection seller. Recent
data from the CDS market suggest that F&F are perceived to have default risk similar to other
large financial institutions.
2.2 Regulatory Controls on Risk
Regulation limits risk-taking through two main mechanisms: restrictions on investments and
minimum capital requirements. F&F’s charter restrict their investments primarily to conventional
mortgages. They predominantly hold and securitize conforming mortgages. The definition of a
conforming mortgage is based on loan size, the loan to value ratio, and property type. The
conforming mortgage ceiling is indexed to house prices and hence has been increasing rapidly.
The conforming limit rose from $252,700 in 2000 to $359,650 in 2005. That limitation excludes
F&F from only about 10 to 20 percent of the residential mortgage market. In fact the fraction of
the market they intermediate has grown more rapidly than the available conforming mortgages, as
the share of non-GSE competitors for conforming mortgages has decreased over time. The loan
to value ratio on a conforming mortgage cannot exceed 80 percent, unless supplemental insurance
or some other permissible guarantee mechanism is obtained. The vast majority of conforming
mortgages are for single family homes, but dwellings with up to four units also can qualify as
conforming.
F&F are required to hold a minimum amount of capital as a buffer against adverse shocks. The
fixed part of the requirement stipulates capital equal to 2.5 percent of on-balance sheet assets, and
.45 percent of off-balance sheet obligations and assets. Additional capital is required if they fail
to pass a stress test that subjects them to several hypothetical large and sustained interest rate
changes over ten years, and also a severe credit event. These capital requirements have recently
become a binding constraint on Fannie Mae, although both firms generally have maintained
slightly more than the regulatory minimum capital. As for commercial banks with deposit
insurance, economic theory predicts that to maximize the value of the implicit guarantee F&F
would manage liabilities so that capital remains close to the regulatory minimum.
11
3. The Model
The options-based approach to modeling credit guarantees is based on the insights of Sharpe
(1976) and Merton (1977), that such insurance can be valued as a put option on the assets of the
underlying firm’s assets. A put option gives the holder the right but not the obligation to sell an
asset at a pre-specified strike price, and will be exercised if the market value of the underlying
asset falls below the strike price. In the case of a firm with just one maturity of zero coupon
guaranteed debt outstanding, the strike price of the option is the face of the debt, and the maturity
of the option equals the maturity of the debt.
This approach, modified to take into account complications such as the term structure of debt
obligations and state-contingent triggers for bankruptcy, is an alternative to traditional predictors
of bankruptcy risk that rely on financial ratio analysis. KMV, a subsidiary of Moody’s, has
invested considerable resources in developing it as a commercial tool, and provides a clear
description of the basic method (Crosbie and Bohn (2003)). Moody’s now uses this information
as an input in some of their credit ratings.
For pricing F&F’s implicit guarantee, our analysis uses Monte Carlo simulation with risk neutral
probabilities, which accommodates a variety of assumptions about debt policy, time variation in
risk, and regulatory regime. Monte Carlo valuation uses the risk-neutral distribution of outcomes,
but we also estimate the true distributions in order to estimate the distribution of possible
observed losses.
3.1 Evolution of Assets.
The standard abstraction for the evolution of asset value is that the expected return on existing
assets reflects the market risk of those assets (e.g., the asset beta), and that the returns are log-
normally distributed.3 In addition, firm assets may increase due to purchases financed with
additional debt and equity issues, or retained earnings. In a risk-neutral representation, returns
are log-normally distributed but on average equal the risk-free rate. The risk-neutral discrete time
representation of the evolution of assets in the Monte Carlo can be represented as:
3 The log normal representation is standard, and allows a simple transformation between the actual and the risk-neutral measure. Some have suggested that financial institutions bear fatter-tailed risks. Although we do not consider this possibility directly, we do consider the possibility of higher asset volatility in the sensitivity analysis in part as a proxy for fatter tails.
12
(1) ⎥⎦
⎤⎢⎣
⎡+−−+=+ hh
AE
grExpAA AAo
otftht εσσδ )5.( 2
where h is the time step, subscripts represent time, E is equity, A is assets, rf is the risk-free rate,
gt is externally financed firm asset growth, δ is the dividend yield on equity (hence 0
0AEδ is the
dividend yield on assets), σA is the volatility of firm assets, and ε is a draw from a standard
normal distribution under the risk neutral probability measure. The same evolution in terms of
the true probability distribution can be written as:
(1a) ⎥⎦
⎤⎢⎣
⎡+−−+=+ hh
AE
grExpAA AAo
otAtht εσσδ ˆ)5.( 2
In equation (1a) ε̂ is a draw from a standard normal distribution under the true probability
measure, and rA is the risk-adjusted required return on assets. These representations for firm
assets should be interpreted as the present value of all expected future cash flows, including those
from on- and off-balance sheet activities. The drift is equal to required returns (equal to the risk-
free rate under the risk-neutral measure, and the risk-adjusted return under the true probability
measure) net of payouts.
Time variation in the assumed volatility of assets can significantly affect cost estimates, with
periods of high volatility having a large influence on guarantee value. Consideration of the
possibility of time variation is important also because of the relatively short historical time series
of available data, and the limited number of large shocks observed. The effect of time variation
in volatility, particularly increased volatility during times of financial distress, is considered in the
sensitivity analysis.
The initial market value and volatility of firm assets must be estimated since it is not directly
observable. The market value of firm assets is the sum of the market value of liabilities and
owners equity. Although many of the liabilities of Fannie and Freddie are liquid and publicly
traded, the complexity of the liability structure makes it difficult to directly estimate their
outstanding market value. Further, the traded debt prices reflect the value of the implicit
13
guarantee, whereas we also are interested in the market value of the liabilities in the absence of
insurance. Using Merton’s framework, we can use options pricing theory to impute the value and
volatility of firm assets from the value and volatility of firm equity. The idea is that equity can be
valued as a call option on the firm’s assets, with a strike price equal to the future book value of
liabilities, according to:
(2) )1()()( 21qTTfrqT eAdNXedNAeE −−− −+−=
(3) 11 )]1()([ −−− −+= qTqT
EA eedNAEσσ
)/(])5.()/[ln( 5.21 TTqrXAd AA σσ+−+=
5.
12 Tdd Aσ−=
where T is the maturity of liabilities, and X is the strike price, q=0
0AEδ is the payout rate of
assets, and all values are as of time 0. Equation (3) comes from the fact that in the Merton model,
.AE EA
AE σσ ⎟
⎠⎞
⎜⎝⎛
∂∂= Given the other parameters, equations (2) and (3) are solved
simultaneously for A and σA.
Although we model asset risk abstractly through asset volatility imputed from equity value and
volatility, it is worth enumerating the types of risk F&F are exposed to. These risks can be
broken into three broad categories: interest rate risk, credit risk, and other risks. An advantage of
the options pricing approach is that stock price volatility is arguably the most comprehensive
measure of risk, and perhaps the only available measure that includes all three sources.
Interest rate risk, and the accompanying prepayment and extension risk that arise due to the
prepayment option on residential mortgages,4 has received the most attention. As discussed by
4 Both prepayment risk and extension risk arise from the option to prepay mortgages. Prepayment risk is due to rapid prepayments in a falling interest rate environment, whereas extension risk results from mortgages remaining outstanding longer than predicted at the time of pricing in a rising interest rate environment. The two risks together give mortgages the property of negative convexity, whereby small changes in interest rates cause a reduction in value relative to an option-free bond with comparable duration.
14
Jaffee (2003), interest rate related risk is absent for the MBS they guarantee, since it is borne by
the holders of those securities. The mortgages held on balance sheet, to the extent they are not
hedged through the debt structure and the use of derivatives, are the source of interest rate risk.
Hedges protect F&F from small to moderate rate changes, but the results of stress tests suggest
that they are exposed to large and rapid movements in rates.
Credit risk is present both from mortgages held on balance sheet, and from the MBS they
guarantee. Credit risk on conforming mortgages is mitigated by the restriction that the loan to
value ratio not exceed 80 percent. On MBS, F&F charge approximately 20 bps for this insurance.
Historically credit losses have been modest, and more than covered by these fees. Nevertheless,
recent concern about regional housing bubbles and the possibility that higher interest rates could
trigger a crash suggest that credit risk could become more significant. It is notable that although
F&F actively manage interest rate risk with derivatives, it does not appear they have tried to
directly hedge this risk, for example by creating and selling derivatives on mortgage credit risk.
Thus, their levered position (via the MBSs they guarantee) in credit risk appears to be entirely
retained.
The “other risks” category is a catch-all for political risk, accounting risk, fraud, liquidity risk,
model risk, counterparty risk in the derivatives market, etc. These other risks are potentially quite
important, although they are emphasized less often in the academic literature and are more
difficult to quantify. Political risks include a weakened public perception of the guarantee value,
which could increase the cost of funds and lower market capital. It also includes the possibility of
legislation that restricts growth or increases competition, reducing franchise value. Seiler (2003)
stresses the importance of political risk, and uses an event study methodology to show its effect
on stock price. Liquidity risk is related to political risk, as the market for Fannie and Freddie
issues might lose liquidity in the event of an unanticipated government action. Accounting
misrepresentations or fraud not only may diminish equity capital, but also can prolong the time
between when a problem arises and is recognized, increasing the severity of losses. The risk
associated with accounting irregularities is evidenced by the recent restatement of $9 billion of
earnings by Fannie Mae, and the subsequent precipitous drop in their stock price.
3.2 Evolution of Liabilities
15
In the simplest form of the Merton model, liabilities have a single fixed maturity and are constant
over the life of the option. This assumption is unrealistic for most firms, and especially so for
highly leveraged financial institutions. Theoretically, debt should be managed to maximize the
value of equity, and closed form solutions for optimal or stationary debt policy have been derived
for a few special cases (e.g., Leland (1994), Collin-Dufresne and Goldstein (2001)). In the case
of insured financial institutions, the standard argument is that holding equity at the regulatory
minimum maximizes the value of the government guarantee, particularly as firms become
distressed. Little is known, however, about how Fannie and Freddie would manage their
liabilities and hedging strategies in the event of sudden financial distress, or the speed with which
they could adjust their liability positions.
To examine the sensitivity of cost estimates to different dynamic liability management strategies,
we assume that the book value of liabilities adjusts towards a target liability to asset ratio at
several different adjustment rates. Liabilities, L, evolve according to:
(4) [ ] tthr
ttthgr
tht AAeLhIeLL dtd /*)( −+= ++ λαγ
where αt is the annual rate of adjustment, which may be state dependent, λ* is the target liability
to asset ratio, and It is an indicator variable that equals one in a period where liabilities are
adjusted, and 0 otherwise. Liabilities grow at a rate rd to cover promised coupons. In addition, a
fraction γ of externally financed growth is supported by debt. This representation applies to both
the actual and risk-neutral measure, but the realized paths differ because the return on debt and
externally financed growth take on different values in each instance.
Computationally it would be straightforward to add volatility to liabilities in this model. We
maintain the assumption of non-stochastic liabilities, however, because the estimated volatility of
assets implicitly captures volatility arising from all sources, including liabilities.
3.3 Modeling the Trigger for Insolvency
In the basic, continuous time Merton model, bankruptcy is triggered by the market value of assets
falling below some trigger value. If the trigger value were equal to the book value of liabilities,
the cost of a credit guarantee would always be zero, since debt holders take over the firm at the
16
point where it equals the value of their claim. In reality managers tend to postpone bankruptcy,
and creditors recover far less than the promised value of their claims. The conditions under
which managers seek the protection of bankruptcy courts varies considerably, leading to wide
variations in recovery rates, even within a single seniority class or industry.
Modeling the bankruptcy trigger for Fannie and Freddie is further complicated by the regulatory
situation. They do not operate under the U.S. bankruptcy code. Their regulator, OFHEO, only
has the powers of a conservator, not a receiver (Carnell (2004)). This means that although
OFHEO has some control, it does not have the authority to close F&F down, nor to pay off
creditors.
Several insolvency triggers are commonly used in models that take into account more
complicated liability structures and trigger strategies (e.g., see Crosbie and Bohn (2003)). One is
that the firm is liquidated when the market value of assets falls below the level of current
liabilities plus half of the book value of long-term liabilities. Another is that the market value of
assets falls below a fraction, sometimes taken to be 70 percent, of the total book value of
liabilities. We consider a variety of trigger levels based on the value of assets relative to book
liabilities. The distinction between long and short-term liabilities is less meaningful for F&F than
for many other firms because of the constant maturity conversion taking place through the
derivatives market, so no distinction is made on that basis.
We assess the cost of a drawn-out reorganization or closure process -- which might also be
described as regulatory forbearance -- in two ways. First, we use the ratio of assets to liabilities
that triggers bankruptcy to represent forbearance, with a higher trigger level representing a more
stringent regulatory policy. Second, following Merton (1978) on deposit insurance, we assume
that the trigger for bankruptcy is only checked periodically. The longer the time between
“audits,” the greater the probability that the financial condition of a distressed firm will have
deteriorated, and the greater the cost to the government contingent upon bankruptcy. The
probability of bankruptcy, however, may be lower under the assumption of less frequent auditing
when asset returns have a positive drift. This offsetting effect makes the net cost of forbearance
in the form of lower frequency audits indeterminate. We consider a variety of audit frequencies
in the sensitivity analysis.
17
An element of the cost associated with a delayed closure procedure is that asset volatility could
increase significantly, for reasons such as unusually volatile markets, reduced availability of
derivatives for hedging, or a purposeful increase in risk-taking to gamble to regain solvency.
This increase in volatility is unlikely to be observed in historical data, both because its occurrence
is a low probability event, and because it is likely to persist for relatively short periods of time
when it does occur. The quantitative analysis below suggests that this may be the most important
cost of forbearance.
4. Results
4.1 Initial Values
Inputs into (2) and (3) to estimate the initial value of firm assets and asset volatility are
summarized in Table 2. All values are based on year-end 2004 data, except the equity volatility,
which is based on its historical average. The Table also shows the resulting estimates of asset
value and volatility. Since the liabilities have multiple maturity dates, the maturity of the option
is based on the average maturity of reported liabilities, and the strike price is the future value of
total reported book liabilities. The volatility of equity is a critical input, serving as a sufficient
statistic for the net effect on risk of all on- and off-balance-sheet activities including interest rate
risk, derivatives used in hedging strategies, and MBS guarantees. Estimated volatility varies
considerably over time. For instance, for Fannie Mae it averages 31 percent from January 4,
1996 to December 31, 2004, but ranges from 16.7 percent to 60 percent (see Figure 4).
Figure 4: Fannie Mae Implied Volatility
00.10.20.30.40.50.60.7
1/4/
1996
1/4/
1997
1/4/
1998
1/4/
1999
1/4/
2000
1/4/
2001
1/4/
2002
1/4/
2003
1/4/
2004
date
vol
implied vol
18
The model generates an estimated asset volatility of only 2.06 percent for Fannie Mae, and 1.92
percent for Freddie Mac. The sensitivity analysis reveals that the cost estimates and distribution
of losses are very sensitive to this parameter.
Table 2: Market Value and Volatility of Assets -- Estimates and Inputs (dollar values in millions) FANNIE MAE FREDDIE MAC Market Value Assets
$1,026,194 $793,670
Volatility Assets 0.0206 0.0192
Market Value Equity
$68,924 $50,740
Volatility Equity 0.3 0.3Book Value Liabilities
$945,000 $731,697
Wtd. Maturity Liabilities
2.65 3.05
Dividend Yield on Equity
0.0225 0.0178
4.2 Base Case
The parameters for the base case simulations are reported in Table 3, with a brief explanation of
what they represent. This case is not necessarily the most likely, but seems a reasonable starting
point. The estimate is based on a 10-year time horizon, mitigating the greater estimation error
and model uncertainty in longer-term projections. Asset volatility is assumed to increase to four
times its normal level when assets fall to 101 percent of liabilities, representing increased
volatility in periods of financial distress. Management and regulatory decisions (debt adjustment
and solvency determination) are evaluated at a quarterly frequency, while assets returns are
calculated at a monthly frequency. Liabilities adjust gradually and asymmetrically towards their
target level -- 80 percent per year adjustment up versus 40 percent per year adjustment down.
The asymmetry reflects that it is more difficult to rapidly reduce liabilities when asset values are
declining than it is to increase them when times are good. To reflect the historically high rate of
asset growth, assets are assumed to grow at a rate equal to their realized return net of dividends,
plus an additional 6 percent annually when the target capital ratio is met or exceeded. The
19
external growth is financed entirely with an increase in debt. When capital is below the target
level there is no additional debt-financed growth.
Table 3: Base Case Parameter Values Short Name Value Description ____ . Fannie Mae FAinit $1,026,194 initial market value of assets ($ millions) FLinit $ 945,000 initial book value of liabilities ($ millions) MVEquity $68,924 initial market value of equity ($ millions) dividend yield 0.0225 Freddie Mac FAinit $793,670 initial market value of assets ($ millions) FLinit $731,697 initial book value of liabilities ($ millions) MVEquity $50,740 initial market value of equity ($ millions) equity dividend yield 0.0178 FAvol 0.0192 firm asset volatility during normal conditions FAvol_h 0.0768 firm asset volatility in high volatility state Common Values rf 0.025 risk free rate rd .0275 promised return on debt FAer_a 0.03307 firm asset expected return (actual) FAer 0.025 firm asset expected return (risk-neutral) FAvol 0.0206 firm asset volatility during normal conditions FAvol_h 0.0824 firm asset volatility in high volatility state FLrate_d 0.4 / 4 quarterly adjustment of liabilities to lower target FLrate_u 0.8 / 4 quarterly adjustment of liabilities to higher target growth 0.06 externally financed growth if enough capital growth_trig .93 if target liability to asset ratio met, then growth growth_debt 1 proportion of external financing that is debt trigger 0.98 bankruptcy trigger assets/liabilities trig_volh 1.01 trigger of assets/liabilities for higher volatility look 4 frequency of checking bankruptcy trigger per year look_l 4 frequency of updating debt FLFAtarget .93 target liability to asset ratio newFLFA 1 proportion of debt financed exogenous asset growth nmonte 20,000 number of Monte Carlo simulations nyear 10 number of years in each simulation run nfreq 12 time steps per year
20
The results of the base case Monte Carlo simulations are summarized in Table 4, where we report
the guarantee value, the risk neutral and actual default probabilities, and the value at risk (VaR) at
the 0.5 percent level under the actual probability measure. The risk neutral default probability is
always greater than the actual default probability due to the effect of market risk; the risk neutral
result is presented to illustrate the magnitude of this difference. The true default probabilities are
consistent with Moody’s historical 10-year cumulative default probabilities for corporate bonds
with comparable ratings -- for instance bonds rated Baa2 have a cumulative default probability
over 10 years of 5.5 percent. Value at risk measures the worst outcome in terms of present value
of the cost of the government payoff at the one percent level over the 10 years of the simulation
period. The VaR is more relevant to the question of systemic risk than the guarantee value, since
it gives a sense of the size of rare but catastrophic outcomes. Figures 5 and 6 show the
distribution of the present value of costs conditional upon default for each firm in the base case.
Table 4: Base Case Results
Guarantee Value ($ billions)
10-year default probability (actual)
10-year default probability (risk neutral)
VaR at .5 percent ($ billions)
Fannie Mae 5.14 .064 .152 74
Freddie Mac 2.78 .042 .115 48
Figure 5: Present Value Cost of Fannie Mae Conditional on
Default
010203040
2000
030
00040
00050
00060
00070
00080
00090
000
1000
00More
($ millions)
perc
ent
21
Figure 6: Present Value Cost of Freddie Mac Conditional on
Default
010203040
2000
030
000
4000
050
000
6000
070
000
More
($ millions)
perc
ent
4.3 Sensitivity and Policy Analyses 4.3.1 Asset Volatility
The experiments reported in Table 5 show that assumed asset volatility is a critical sensitivity.
The guarantee cost, the probability of default, and the VaR all increase rapidly in volatility over
the range considered. Results for both firms are reported for a fixed 2.5 percent and 3 percent
asset volatility. All other parameters are as in the base case.
Table 5: The Effect of Increased Asset Volatility
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie Mae (.025 vol) 9.60 .130 100
Freddie Mac (.025 vol) 7.24 .126 80
Fannie Mae (.03 vol) 15.43 .215 126
Freddie Mac (.03 vol) 12.03 .216 97
An alternative to higher steady state volatility that increases guarantee value without significantly
increasing the probability of default is to increase the conditional volatility when the enterprises
22
become distressed. In general, higher conditional volatility might be attributable to the same
factors that caused financial distress, or it could result from deliberate risk-taking in an effort to
avoid insolvency. To examine this effect, the non-distress volatilities and all other parameters are
set to base case values. In the first variation conditional volatility is held constant at the base case
non-distress level. In the second variation, for an asset to liability ratio between the default
trigger of 98 percent and 101 percent, volatility is assumed to increase six-fold for each firm.
These values bracket the base case, in which volatility increases fourfold for the same range of
liability ratios. The results are reported in Table 6.
Table 6: High Volatility Conditional on High Leverage
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
observed average vol
Fannie (0x high vol) 4.32 .020 31 .0206
Freddie (0x high vol) 2.40 .009 19 .0192
Fannie (6x high vol) 5.39 .065 96 .0210
Freddie (6x high vol) 2.84 .043 63 .0195
What is most striking about results in the high conditional volatility case in Table 6, as compared
to the results with the smaller but constant increases in volatility considered in Table 5, are
similarly high VaRs but much lower 10-year default probabilities. The difference is explained by
the fact that higher conditional volatility tends to make losses more severe when bankruptcy
occurs, but distress events remain rare. Also noteworthy is that the observed average volatility
(calculated across simulations and time periods) is only slightly higher than the volatility during
normal periods (last column in Table 6). The low observed volatility occurs because periods of
heightened volatility are rare and short-lived. This suggests that time variation in volatility may
be an important, but intrinsically unobservable, factor driving guarantee costs and systemic risk.
4.3.2 Liability Rules
How the fixed portion of liabilities (equated initially to the book value of on-balance sheet debt)
should vary over time with firm asset value is an open but important question. Mathematically it
affects the results because it is the reference point for the bankruptcy trigger. In the base case, the
difference in difficulty of adjusting debt up in good times versus down in bad times is reflected in
differential adjustment speeds of 80 percent per year towards the target versus 40 percent per year
Deleted: 1
23
towards the target. The sensitivity analysis reported in Table 7 shows the effect of two
alternatives: a symmetric rate of adjustment up and down of 25 percent, and a severe asymmetry
of 85 percent up and 15 percent down. As expected, greater asymmetry, and reducing the rate at
which liabilities can be reduced with or without asymmetry, increases the guarantee cost
significantly – for these parameters by as much as a factor of two relative to the base case.
Table 7: Alternative Debt Adjustment Rules
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie (symmetric, +.25/-.25) 7.20 .075 71
Freddie (symmetric, +.25/-.25) 4.50 .056 50
Fannie (asymmetric, +.85/-.15) 9.96 .10 79
Freddie (asymmetric, + .85/-.15) 6.26 .075 54
4.3.3 Changing Capital Requirements
The effect of altering capital requirements can be represented by a change in the target ratio of
liabilities to assets. In the base case the target ratio is set to .93, slightly higher than the initial
estimated ratio. Actual capital requirements are more complicated than a simple ratio of the
market value of equity to the market value of assets, as they depend on book values and stress test
results. How tightly management can and does maintain a target ratio also is not observable.
Table 8 shows the effect of increasing the assumed target ratio to .95 and decreasing it to .91,
with all other parameters as in the base case. As would be expected of such highly levered
institutions, relatively small changes in the target leverage ratio have an enormous impact on the
guarantee value and risk exposure, suggesting that this is a powerful policy lever for controlling
government risk exposure.
Table 8: Changing Capital Requirements
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie (target L/A = .91) 1.93 .023 54
Freddie (target L/A = .91) 1.01 .014 33
Fannie (target L/A = .95) 11.14 .149 97
Freddie (target L/A = .95) 6.70 .108 70
24
4.3.4 Growth and Horizon
In the past decade F&F’s portfolio growth rate exceeded that of the conforming mortgage market
as they captured an increasing market share. Growth rates going forward likely will be lower,
both because market share is bounded and because of regulatory pressures to restrain growth. In
the base case we assume that both companies grow according to the rate of return on their assets
net of dividends, which averages about 3 percent, and that if the capital ratio is at or above its
target, assets increase an additional 6 percent, funded entirely by new debt issues. A natural
question is what happens to estimated costs if debt-funded growth is higher or lower than initially
assumed? Table 9 reports what happens when externally financed growth is assumed to be 4
percent or 8 percent, with all other parameters as in the base case. While guarantee value and
VaR both increase with the growth rate, the increases are modest. The small effect can be
attributed to the assumption that externally financed growth only occurs if the target capital ratio
is satisfied.
Table 9: Varying Exogenous Growth
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie (4% growth) 4.58 .057 68
Freddie (4% growth) 2.56 .039 48
Fannie (8% growth) 5.38 .068 79
Freddie (8% growth) 2.88 .043 52
The analysis focuses on a 10-year horizon to avoid the greater approximation errors at longer
horizons. For comparison to other studies, and to illustrate the effect of horizon on cost, Table 10
reports results under the base case assumptions, but with a 25-year horizon. In comparison to the
10-year horizon, the guarantee value increases by a much larger percentage than the VaR because
while the number of bankruptcy events increases with horizon, the severity of the events is
limited by the assumption that liabilities revert toward a target level and by the closure rule.
25
Table 10: Costs Over 25 Year Horizon
Guarantee Value ($ billions)
25-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie Mae 17.41 .199 89
Freddie Mac 10.67 .136 60
4.3.5 Forbearance
In the base case regulators are assumed to monitor the enterprises quarterly, and to shut them
down if the ratio of assets to liabilities falls below the bankruptcy trigger of .98. One way to
model greater forbearance is to decrease the frequency at which the bankruptcy trigger is
monitored. Another approach is to lower liability to asset ratio that serves as the bankruptcy
trigger.
The effects, shown in Table 11, of varying the monitoring frequency are based on a 25-year
horizon. Table 10 serves as the base case for comparison, as it is also for a 25-year estimation
period. The longer horizon permits a more accurate assessment of the effect of changing the
monitoring frequency. The results indicate that increasing the frequency of monitoring
dramatically reduces the VaR – going from semi-annual to monthly monitoring more than cuts it
in half. With more frequent oversight, regulators are able to cut off rapidly mounting losses,
significantly reducing the likelihood of a catastrophic event. Increasing monitoring frequency,
however, has a relatively small effect on the estimated guarantee value. In fact, for some
parameters, increasing monitoring frequency has the effect of slightly increasing guarantee value.
The reason is that while more frequent monitoring tends to reduce costs conditional on hitting the
trigger, an offsetting effect is that it increases the frequency with which the trigger is hit.
Table 11: Varying Monitoring Frequency
25-year Guarantee Value ($ billions)
25-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie (monthly) 16.72 .230 54
Freddie (monthly) 10.77 .160 37
Fannie (semi-annually) 17.83 .172 121
Freddie (semi-annually) 10.96 .122 80
26
For the bankruptcy trigger, we maintain all base case assumptions (returning to a 10-year horizon
and quarterly monitoring), but bracket the base case assumption that an asset to liability ratio of
.98 triggers bankruptcy, setting the trigger to .97 and .99. As with the frequency of monitoring,
and for the same reasons, changing the bankruptcy trigger has an insignificant effect on guarantee
value, but a very large impact on the VaR and the probability of catastrophic losses.
Table 12: Varying Bankruptcy Trigger
Guarantee Value ($ billions)
10-year default probability (actual)
VaR at .5 percent ($ billions)
Fannie (asset/liability .97) 4.63 .051 85
Freddie (asset/liability .97) 2.52 .035 62
Fannie (asset/liability .99) 4.43 .072 52
Freddie (asset/liability .99) 2.61 .049 33
4.4 Comparisons to Previous Studies
Many of the results in the literature cannot be directly compared because they vary with regard to
the time period covered, whether the estimate is a present value or an annual flow number, and
exactly what the cost represents. Nevertheless, it is useful to make some comparisons of these
estimates with those of other studies.
Several authors have estimated the value of the implicit government guarantee by comparison of
yields on F&F debt with issues from similarly rated financial institutions of equal maturities.5
The subsidy on MBSs guaranteed was similarly found by looking at comparable guarantees made
by private entities. For instance, CBO (2004a) reports an estimated present value subsidy of
$12.6 billion for Fannie Mae on debt and MBS, and $5.9 billion for Freddie Mac. The CBO
numbers represent the incremental value of a year of new business, rather than the value of a 10-
year guarantee on the enterprises. Passmore (2005) reports a present value over 25 years in the
range of $122 to $182 billion as the subsidy to Fannie and Freddie. His estimates are
conceptually similar to the ones reported here, but considerably larger. The closest comparison is
with the results in Table 10, which shows a combined guarantee value of $28 billion over 25
years, or approximately 23 percent of F&F’s combined market capitalization.
5 Ambrose and Warga (2002) and Nothaft (2002) estimate the funding advantage of the GSEs.
27
Several Fannie Mae papers have examined risk using volatility-based methods. Stiglitz et. al.
(2002) conclude that the cost of an implicit guarantee to the government would not exceed $200
million, which is more than an order of magnitude smaller than our estimates. One reason for the
discrepancy is that they rely on the relatively benign historical time series on interest rates and
credit risk of the post-WWII period, rather than using forward-looking stock market prices as the
basis for calibrating volatility. They do not describe the details of their valuation model, but it
appears that they do not consider the possibility of time variation in volatility, nor the possibility
of changing behavior in periods of distress. Hubbard’s (2004) approach has similarities with the
one taken here, although it relies on a different underlying model of assets and liabilities. He
focuses on default probabilities and losses at a one-year horizon, so the analysis cannot be used to
assess the present value of the guarantee.
A possible explanation for the higher subsidy values that emerge from spread-based analyses
versus options-based methods is that the benefit of the implicit government guarantee to the GSEs
is greater than the cost of expected defaults to the government. The difference arises, for
instance, because the agency classification of the debt allows regulated financial institutions to
hold less capital against these investments, and because liquidity, also a valuable if hard to
quantify commodity, is enhanced. The fact that the market places value on other attributes that
accompany the implicit government guarantee means that from an opportunity cost perspective,
the cost to the government includes these other benefits created, and also is greater than the cost
of expected defaults. The estimates here, then, should be considered a conservative estimate of
the cost to the government of the implicit guarantee.
5. Summary and Further Discussion
The analysis suggests several conclusions about the cost and risk of the implicit government
guarantee to F&F. As expected, the present value of the guarantees are far smaller than the
potential losses from a catastrophic outcome, as represented here as by the .5 percent value at risk
of the present value of 10-year costs. The base case estimates show guarantee values over 10
years that total 7.9 billion. The VaR is $74 billion for Fannie, and 48 billion for Freddie. A novel
feature of this analysis is to quantify the effect of correlation between volatility and financial
distress, a feature that significantly increases estimated costs and risk exposure. The analysis also
demonstrates that such a correlation may be present but unidentifiable in historical data because
periods distress leading to high volatility are rare and relatively short-lived. The policy options
28
considered – strengthening capital requirement or increasing oversight – are shown to have very
different effects. Tighter capital requirements could significantly reduce guarantee values, but
have a smaller effect on catastrophic outcomes. Increased oversight in the form of more frequent
monitoring or a tighter shut-down trigger has a minimal effect on guarantee value, but could
significantly reduce the probability of catastrophic losses.
It is important to emphasize what these estimates do, and do not, measure. The estimates
represent the market value of providing credit insurance to F&F’s debt-holders, but not the
economic efficiency loss or benefit resulting from the subsidy. As a first approximation, the
subsidy is a pure transfer to the stakeholders6 in F&F from the government, and hence from
taxpayers at large. The size of any social efficiency losses or gains, such as whether the subsidy
causes overinvestment or reduces underinvestment in housing, cannot be inferred from these
numbers; a fundamentally different type of analysis would be required to assess such questions.
It also should be emphasized that the options-pricing approach takes a narrow view of the value
of the guarantee, abstracting from benefits such as added liquidity or lower associated capital
requirements for the regulated institutions that invest in their securities that increase the market
value of GSE securities. Hence, these estimates are lower than the cost to the government in
terms of opportunity cost, which is a conceptually broader measure of the benefit conferred.
The absolute size of the reported numbers suggests that while financial distress at F&F could be
costly, it is unlikely to be large enough to severely disrupt financial markets. However, poor
management of an evolving crisis could lead to much higher costs and greater market disruption
than is captured in this exercise. As a point of reference, the combined value at risk in most of
the scenarios considered is less in real terms than the cost of the S&L crisis in the 1980s.
To construct a less stylized model, or to better calibrate and evaluate this one, would require
information not currently reported by Freddie or Fannie. Providing more information about
duration and convexity would significantly improve transparency, and imposes a relatively small
additional reporting requirement. Currently, neither Fannie nor Freddie report the separate
duration of assets and liabilities, only the gap between them. Neither reports convexity, either in
public disclosures or privately to OFHEO. The negative convexity associated with mortgages
6 Many of the spread-based analyses cited earlier attempt to tease out the incidence of the subsidy between shareholders and homeowners, usually using information on the spread between conforming and jumbo mortgages. The analysis here does not address this issue.
29
implies that the duration gap is only informative about risk for very small changes in interest rate.
It also implies that losses will increase at a faster than linear rate for large interest rate changes.
The convexity gap is a measure of this divergence that, together with the duration gap, would
provide a more reliable estimate of interest rate and prepayment risk.
Although mortgages are highly collateralized and historically credit losses have been small, F&F
have a highly leveraged exposure to credit risk that is not hedged. Other financial institutions,
including insurers, use reinsurance markets, or increasingly, credit default swaps, to better spread
such risks. An option that has not received much attention is to encourage credit hedging by
F&F.
In considering how the regulation of the GSEs should be changed to limit potential systemic risk,
a number of fundamental considerations that are beyond the scope of this study must also be
taken into account. One is whether government support for Fannie and Freddie on net stabilizes
the housing market. While the increased liquidity of the mortgage market increases the supply of
capital to housing in normal times, it may also encourage excessive investment in housing or
inflation in housing prices that exacerbates problems during periods of heightened risk. Another
open question is whether there are mechanisms that would allow the government to credibly
avoid or lower the expected cost of interventions, for instance by offering a more limited but
explicit guarantee financed by premiums charged to the enterprises.
30
References
Ambrose, Brent, and Arthur Warga. 2002. Measuring potential GSE funding advantages. Journal of Real Estate Finance and Economics 25(2/3): 129-150. Carnell, Richard S. 2005. “Handling the Failure of Fannie Mae and Freddie Mac,” Conference on Receivership Powers, American Enterprise Institute, Discussion Draft Collin-Dufresne, P. and R.S. Goldstein, 2001, “Do credit spreads reflect stationary leverage ratios?”, Journal of Finance, 1929-1957. Congressional Budget Office 2001, “Federal Subsidies and the Housing GSEs” Congressional Budget Office 2004a, “Updated Estimates of the Subsidies to the Housing GSEs” Congressional Budget Office 2004b, “Estimating the Value of Subsidies for Federal Loans and Loan Guarantees” Crosbie, Peter and Jeff Bohn 2003, “Modeling Default Risk,” Moody’s KMV White Paper; available at http://www.moodyskmv.com/research/whitepaper/ModelingDefaultRisk.pdf Falcon, Armando 2004. Statement before the Committee on Banking, Housing, and Urban Affairs, U.S. Senate Feldman, Ron. 1999. “Estimating and managing the federal subsidy of Fannie Mae and Freddie Mac: Is either task possible?” Journal of Public Budgeting, Accounting, and Financial Management 11 (Spring): 81–116. Frame, W. Scott and Lawrence J. White. 2005. “Fussing and Fuming over Fannie and Freddie: How Much Smoke, How Much Fire?” forthcoming, Journal of Economic Perspectives Hubbard, R. Glenn, 2004. “The Relative Risk of Freddie and Fannie,” Fannie Mae papers, Vol. III, Issue 3. Jaffee, Dwight. 2003. “The interest rate risk of Fannie Mae and Freddie Mac,” Journal of Financial Services Research, 24(1): 5-29. Kane, Edward J. and Chester Foster. 1986. “Valuing conjectural government guarantees of FNMA liabilities,” In Proceedings: Conference on Bank Structure and Competition. Chicago: Federal Reserve Bank of Chicago. Leland, Hayne E., “Corporate Debt Value, Bond Covenants, and Optimal Capital Structure”, Journal of Finance, 49 (4), 1994, 1213-52. Merton, Robert C., “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates”, Journal of Finance, 29 (2), 1974, 449—470. Merton, Robert C., “An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance: An Application of Modern Option Pricing Theory, Journal of Banking and Finance, 1(1), 1977 (June), 3—11.
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Naranjo, Andy and Alden Toevs. 2002. “The effects of purchases of mortgages and securitization by government sponsored enterprises on mortgage yield spreads and volatility,” Journal of Real Estate Finance and Economics. 25 (September-December): 173-195 Nothaft, Frank E., James E. Pearce, and Stevan Stevanovic. 2002. “Debt spreads between GSEs and other corporations,” Journal of Real Estate Finance and Economics 25 (September-December): 151:172. Passmore, Wayne. 2005. “The GSE implicit subsidy and the value of government ambiguity,” Real Estate Economics, forthcoming Seiler, Robert S. 2003. “Market discipline of Fannie Mae and Freddie Mac: How do share prices and debt yield spreads respond to new information?” Office of Federal Housing Enterprise Oversight Working Paper 03-4. Sharpe, William F. (1976), “Corporate Pension Funding Policy”, Journal of Financial Economics, 3(3), (June), 183—193. Stiglitz, Joeseph E., Jonathan M. Orsag and Peter Orsag, 2002, “Implications of the New Fannie Mae and Freddie Mac Risk-Based Capital Standards,” Fannie Mae papers, Vol 1, Issue 2.
